The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Stromule formation is dependent upon plastid size, plastid differentiation status and the density of plastids within the cell

Stromules are motile extensions of the plastid envelope membrane, whose roles are not fully understood. They are present on all plastid types but are more common and extensive on non-green plastids that are sparsely distributed within the cell. During tomato fruit ripening, chloroplasts in the mesocarp tissue differentiate into chromoplasts and undergo major shifts in morphology. In order to understand what factors regulate stromule formation, we analysed stromule biogenesis in tobacco hypocotyls and in two distinct plastid populations in tomato mesocarp. We show that increases in stromule length and frequency are correlated with chromoplast differentiation, but only in one plastid population where the plastids are larger and less numerous. We used tobacco hypocotyls to confirm that stromule length increases as plastids become further apart, suggesting that stromules optimise the plastid-cytoplasm contact area. Furthermore, we demonstrate that ectopic chloroplast components decrease stromule formation on tomato fruit chromoplasts, whereas preventing chloroplast development leads to increased numbers of stromules. Inhibition of fruit ripening has a dramatic impact on plastid and stromule morphology, underlining that plastid differentiation status, and not cell type, is a significant factor in determining the extent of plastid stromules. By modifying the plastid surface area, we propose that stromules enhance the specific metabolic activities of plastids. This is an electronic version of an Article published in The Plant Journal, August 2004, Volume 39, pp. 655-667. Copyright 2004 Blackwell Publishing Ltd and The Society for Experimental Biology.

Similarity solutions of a Becker-Döring system with time-dependent monomer input

We formulate the Becker-Döring equations for cluster growth in the presence of a time-dependent source of monomer input. In the case of size-independent aggregation and ragmentation rate coefficients we find similarity solutions which are approached in the large time limit. The form of the solutions depends on the rate of monomer input and whether fragmentation is present in the model; four distinct types of solution are found.